With the advent of technologies and services related to teleconferencing and digital image storage, considerable progress has been made in the field of digital signal processing. As will be appreciated by those skilled in the art, digital signal processing typically relates to systems, devices, and methodologies for generating a sampled data signal, compressing the signal for storage and/or transmission, and thereafter reconstructing the original data from the compressed signal. Critical to any highly efficient, cost effective digital signal processing system is the methodology used for achieving compression.
As is known in the art, data compression refers to the steps performed to map an original data signal into a bit stream suitable for communication over a channel or storage in a suitable medium. Methodologies capable of minimizing the amount of information necessary to represent and recover original data are desirable in order to lower computational complexity and cost. In addition to cost, simplicity of hardware and software implementations capable of providing high quality data reproduction with minimal delay are likewise desirable.
At present, the next standard of JPEG 2000 (Joint Photographic Experts Group) systems for still images proposes algorithms which use a wavelet to achieve decomposition of an input signal. In systems utilizing a wavelet, the data is typically divided through low pass and high pass filters. The implementation of wavelet filters is typically achieved using a filter bank and, in many instances, involves several levels of filtering. Filter bank operation is often implemented through numerous multiplications and additions between the wavelet coefficients and the input data. The process of implementing filter banks can be time consuming unless very fast multipliers are used. Such multipliers typically utilize parallel processing, which requires the use of fast clocks with higher current consumption as well as requiring larger chip areas in their implementation.
Some prior art filter banks have eliminated multipliers through the use canonical signed digit(s) (CSD). CSD is a powers of two representation of an integer (e.g., 9=23+20). One such filter bank is described by Horng et al. in an IEEE article entitled “The Design of Low Complexity Linear-Phase FIR Filter Banks Using Powers-of-Two Coefficients with an Application to Subband Image Coding,” Vol. 1, No. 4, December 1991. This prior art system develops a method for obtaining an optimal representation for the low pass filter and high pass filter in the filter bank. The authors' premise is how close the CSD representation of the filter coefficients is to the infinite precision design. Hence, based on this language, Horng et al., have developed “an objective function that will yield good filtering performance while adhering to” a constraint equation which embodies the well known perfect reconstruction condition. This constraint equation is based on an imposed pure-delay requirement implied by perfect reconstruction. To overcome the non-linearity in this equation, low pass filter coefficients are first restricted to CSD without any constraint, then a suitable set of high pass CSD coefficients are obtained by using a complex optimization algorithm such that the constraint equation is met.
This invention further reduces the set of the optimal representation of CSD coded coefficients of the filters in the filter bank, by adaptively selecting a subset of the number of CSD terms.
While certain wavelet transforms are closely linked to the two-band (or two-channel) perfect reconstruction (i.e., lossless) filter bank, this is not always the case. Wavelet based CODECs are often used in both lossless (perfect reconstruction) and lossy (for example systems involving quantization) digital data systems. Quantization refers to the technique of taking a bit stream of data and compressing it for later reproduction. In most data compression applications, the presence of quantization in a lossy system implies a rate-distortion performance, which usually bounds the quality of the recovered image. Thus, a pure-delay requirement on the design and representation of the wavelet coefficients is too restrictive, often resulting in implementations that are more complex than required. The further reduction in the number of terms used in the CSD representation proposed by this invention is based on a system, which includes some method for lossy coding.
There is a need for a method and apparatus which provides improved wavelet filtering for both lossy and lossless digital data systems. Such wavelets should be implemented so as to minimize current drain and reduce computational intensity.